Vagary (N): whim, caprice
This word comes form the “Latin” root “vagary” which means “to wander, or to roam”, this root can be further hacked up as “vagus” which means wandering. Guys and gals do you remember the model by name “Caprice Bourret”, create a mnemonic relating her vagaries with the word vagrant, but don’t forget it is the whimsical behavior that relates to the word and not her beauty. HAHAHA
If you want to read more about her follow this link:
http://en.wikipedia.org/wiki/Caprice_Bourret

Contextual example:
Because this species of plant was subjected continuously to the vagaries of nature it became adapted to even rougher atmospheric conditions.

Vagrant (adj): stray, random.

As “vagari” means “to wander”, something that wanders is bound to move from anywhere to anywhere that’s why the meaning develops as “stray, random”.

Contextual example:
He controlled his vagrant thoughts by practicing Pranayma and Yoga.

Vagrant (N): homeless wanderer.

Contextual example:
Everybody thought that the shabby stranger was a vagrant, but none knew that he was their king in disguise.

Vagabond (N): wanderer, tramp.

Contextual example:
Sometimes the CEO felt that he should put all his business aside and enjoy life being a vagabond, chasing his vagrant impulses.

Vague (adj): Not clearly expressed, inexplicit, obscure.

Contextual example:
The CEO was a bit vague about the specifics of the action plan, which was to be followed for tripling the profits of the firm.